The correct option is B |z−w|2≤(|z|−|w|)2+(argz−argw)2
We know that, |z−w|2=|z|2+|w|2−2Re(z ¯¯¯¯w )
=|z|2+|w|2−2|z||w|cos(α−β),
(where α=argz, β=argw)
So, |z−w|2=(|z|−|w|)2+2|z||w|(1−cos(α−β))
≤(|z|−|w|)2+4sin2(α−β2)2 (∵|z|≤1,|w|≤1)
≤(|z|−|w|)2+4(α−β2)2 (∵sinθ<θ for θ ∈(0,π2))
≤(|z|−|w|)2+(α−β)2
≤(|z|−|w|)2+(argz−argw)2